SOLUTION: f (x)=6x^2+x-2. Find the y and X intercepts Determine the maximum or the minimum point of the function Sketch the graph of f (x)=6x^2+x-2

Question 987386: f (x)=6x^2+x-2.
Find the y and X intercepts
Determine the maximum or the minimum point of the function
Sketch the graph of f (x)=6x^2+x-2
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
.

.
Set x=0 to find y-intercept:

ANSWER: The y intercept is (0,-2)
.
Set y=0 to find x-intercept:
0=6x^2+x-2
.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=49 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.5, -0.666666666666667. Here's your graph:

.
ANSWER: The x intercepts are (0.5,0) and (-2/3,0)
.
Derivatives:
.
' Set this to zero to find critical point.
'' This is positive so we will find the minimum.
.
Find critical point:
Set first derivative=0 to find x value of critical point
'

.
Solve for f(-1/12) to find the y value of critical point:

y=-2 6/144=-2 1/24
.
Critical point (turning point, minumum): (-1/12,-2 1/24)
.
GRAPH:
.

RELATED QUESTIONS
Determine the maximum or minimum value of the quadratic function.... (answered by stanbon,rapaljer)

Determine whether the graph of y = x^2 − 6x + 3 has a maximum or minimum point,... (answered by stanbon)

Determine whether the given quadratic function has a minimum value or maximum value. Then (answered by Fombitz)

determine whether the given quadratic function has a minimum or maximum value. then find... (answered by Boreal)

Determine whether the given quadratic function has a maximum value or minimum... Then... (answered by lwsshak3)

please help of this 1. Given the function Y=-(x+1)^2+3 a) Find the X- and Y-... (answered by josgarithmetic)

Determine the coordinates the minimum point from the graph of the quadratic function... (answered by MathLover1,MathTherapy,ikleyn)

Determine whether the function f(x) = -x^2-2x-7 has a maximum or minimum value and find... (answered by HyperBrain)

Graph the function. Find the vertex, line of symmetry, and maximum or minimum value.... (answered by lwsshak3)